LA-7833-MS
Informal Report
C.3
ClC-l4 REPORT COLLECTION
REPRODUCTION COPY
Fireball Shape as a Height-of-Burst Diagnostic
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UNITED STATICS
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CONTRACT W-740 B-ZNG. 36
LA-7833-MS InformalReport
Swcial Distribution Issued: June 1979
Fireball Shape as a Height-of-Burst Diagnostic
Eric M. Jones Jeffrey D. Colvin*
— ,
GEG&G, Inc., P.O. Box 809, Los Alamos, NM 87544.
i
FIREBALL SHAPE AS A HEIGHT-OF-BURST DIAGNOSTIC
by
Eric M. Jones and Jeffrey D. Colvin
ABSTRACT
The shock wave produced by an atmospheric nuclear fireball reflects from the ground and strikes the bottom of the glowing fireball at the time when the sum of the fireball radius and the shock radius equals twice the burst height. RADFLO calculations have been used to define the function R(fireball) + R(shock) = f(Y,t). Fireball shape information is used to determine the time when shock/fireball interaction occurs and to derive the height-of-burst.
I. INTRODUCTION
The evolution of an atmospheric nuclear fireball is governed by the weapon
mass, yield and configuration, the pressure and temperature of the atmosphere,
and the height-of-burst. In many military applications heights-of-burst are low
enough that interaction between the glowing fireball and the shock wave
reflected from the ground surface occurs long before buoyancy forces become
important. In many of these applications, the desired effect is a sensitive
function of burst height. Real-time height-of-burst data may be of potential
value, particularly if the data can be determined from a single observing
station.
Let us suppose that an atmospheric nuclear burst of unspecified y-
occurs at an unknown range from a properly instrumented observing station.
parameters to be determined are yield, range, azimuth, and height-of-burst.
propose that all four parameters can be determined with two primary instrum[
eld
The
We
nts
and a small computer or processor. The two instruments are a bhangmeter and a
fast read-out, “real-time” imaging array. The bhangmeter is used to determine
minimum time and, hence, the yield while real-time fireball shape information
provides the three remaining parameters.
II. METHOD
We presume that bursts of interest will be low-mass airbursts. The
assumption of low mass assures that we will be dealing with weapons with high
radiating temperatures and that the early fireball growth will be virtually
spherical. U.S. atmospheric tests of weapons in massive towers or suspended
from balloons show considerable asymmetries and brightness irregularities even
at very late times. Air drops of low mass-to-yield ratios all produce very
spherical fireballs.
The yield is determined from time-of-minimum measured with a bhangmeter.
During the blast wave phase of expansion the radius is closely
approximated by
R= 301 (Y/P)l/5 t*/5, (1)
where R is the radius in meters; Y the yield in kilotons; p the ambient
atmospheric density in milligrams per cubic centimeter; and t the time in
seconds. Because the
acceptable to assume a
as yet to be determined
Imaging data can
radius is so insensitive to density it will probably be
value for the density. An iterative scheme based on the
burst height could be adopted if deemed necessary.
be used to derive the time histories of the vertical and
horizontal angular diameters. Knowledge of the yield and the horizontal angular
diameter leads directly to the range and, from the position of the image on the
detector, azimuthal data is obtained.
.
i
The final piece of data, the height-of-burst, can be obtained from
comparison of the two angular diameters.
The fireball expansion will be tspherical until the reflected shock wave
strikes the glowing fireball. Shortly after shock/fireball interaction the
bottom surface of the fireball is severely flattened. Before the interaction,
the ratio of the vertical diameter to the horizontal diameter is approximately
equal one but as the interaction proceeds the ratio drops sharply. Analysis of
the time history of the diameter ratio provides a time-of-interaction which can
then be used to derive the height-of-burst.
I
III. HEIGHT-OF-BURST SCALING DATA
The LASL one-dimensional, spherical, radiation transport/hydrodynamics
program RADFLO has been very successful in calculating atmospheric nuclear
fireball evolution. Fireball and shock radii produced by the program are in
good agreement with data.
We assume with some confidence that the shock/fireball interaction occurs I
when
‘SH = 2H-RFB (2)
where RSH is the shock radius, RFB is the fireball radius and H is the burst
height (Figure 1). We recognize that the reflected shock traverses slightly
heated air before striking the fireball and that the interaction actually occurs
slightly before the time given by equation (2). However, we expect that the
effect is small compared to likely yield uncertainties.
A series of RADFLO calculations have been made for bursts of various
yields at sea-level density (1.2x10-3 gcm-3). The fireball radius was chosen as
the 0.2 eV temperature contour while the shock radius was chosen as the location
of maximum density in the computed shock profile. Positional uncertainties are
about one cell width or about one percent of the radius. These data were used
to compute time histories of RSH + RFB. The results are presented in figure 2.
I
3
I
UNCLASSIFIED
Fig. 1
Determination of the time of fireball/shock interaction permits derivation of burst height.
1(?
BLAST WAVE
~ REGIME
fa
102
,:2 ,~-1 d
TIME (see)
Fig. 2
The fireball radius (RFB) and shock radius (RsH) are calculated with RADFLO. Knowing the yield and time of fireball/shock interaction gives
2H = RFB+RSH from the graph. See the text for a further discussion of this figure.
UNCLASSIFIED
.
&
The curves in figure 2 are labeled with the parameter 301 (Y/P)l/5. The
curves, in ascending order, correspond to sea-level bursts with yields of 1,
3.5, 12, 32, 75, 200, 800, and 1600 kilotons.
The plane of figure 2 is divided into three phenomenological regions.
During the early fireball expansion the air immediately behind the shock has
been heated to greater than 0.2 eV and the shock and fireball radii are
identical. During this blast wave phase both radii are closely approximated by
I
equation 1. At a time given by the leftmost dashed line, the weakened
no longer capable of heating air above 0.2 eV and the shock “detaches”
fireball.
shock is I
from the
At very late time, fireballs which have not yet undergone shock inter-
action are deformed by buoyancy forces. The vertical deformation is
approximately given by
AR = gtz (3)
where g = 9.8 m S-2 is the gravitational acceleration. During the late fireball
evolution the fireball radius reaches a maximum and slowly declines thereafter
while the shock wave velocity approaches the sound speed. (The upward curvature
of the RFB + RSH lines is a result of this behavior.) The maximum fireball
radius is designated as RM. If the buoyant deformation exceeds a few percent,
the height-of-burst analysis suddenly becomes more complex. This buoyancy
regime has been delineated by the AR = 0.02 RM line at the right of figure 2.
The graph
determined from
diameters. The
the burst height
Iv. TEST DATA
is used as follows: the time of shock/fireball interaction is
the history of the ratio of the vertical to horizontal
known yield is then used to interpolate between the curves and
is read as half the sum of the two radii.
We have analysed photographic
tests conducted in Nevada for which
data for seven U.S. atmospheric
unclassified yields are available
nuclear
and one
Pacific test. All were low mass air drops. The relevant data for the seven
events with the unclassified yields are given in Table I. All had p= 1.OX1O-3
5 I
gcm-3. The histories of the ratio of the vertical and horizontal diameters are
given in figures 3 through 9. For the purpose of this paper we have m&rely
estimated the interaction time as the time of a significant, sustained drop of
the diameter ratio. The range of the estimated interaction time (ti) for each
event is given in Table 1,
The derived burst heights (HD) are plotted against the actual heights in
figure 10. Clearly, the errors are less than 50 meters in all cases. The
relative errors are given in Table I for the seven unclassified events. Al 1
eight events have errors less than 20 percent.
TABLE I
THE SEVEN NTS AIR DROP EVENTS EXAMINED IN THIS STUDY
NAME
GRABLE
FIZEAU
CLIMAX
TS-DOG
BJ-EASY
BJ-CHARLIE
WASP-PRIME
T&-
15
11.4
62.8
19
31
14
3“
7%
160
152
407
317
401
345
222
65
68
102
119
128
143
157
t“
its
.075-.1
.08-.1
.3-.45
.4-.5
.3-.5
.45-.5
.4-.5
518
490
689
543
599
511
375
180
180
415
350
368
328
224
HD-H
T
.13
.18
.02
.10
-.08
-.05
-.01
v. REFINEMENTS
This simplistic discussion of shock/fireball interactions has led to
fairly accurate burst height estimation for eight nuclear tests. Some fine
tuning of the model may improve the results and/or indicate presently
unidentified limitations.
1) For bursts which suffer ground interaction before minimum time, ~lN is
a function of burst height. Calculational work has been done to define the
variation with height for a series of bursts with the IVY-KING yield (540 kt).
These results are plotted in Figure 11. The analysis routines for determining
burst height should include an iterative scheme to account for modified yield
estimates at low burst heights.
2) Numerical tests of existing photographic data must be made to determine
the effects of finite resolution elements and threshold sensitivities on the
results. We imagine that there is a tradeoff between fine resolution and
accurate diameter ratio measurements on the one hand and reduced integration
times with coarse grids on the other. We intend to perform computer simulations
of selected data frames to quantify these effects, and to determine the
limitations imposed by the frame time resolution of typical imaging devices (RJ
1/30 s).
3) Similarly, atmospheric attenuation and decreasing intensities with
increasing range may introduce errors. Fireballs which suffer interaction after
a few times second-maximum do not have particularly well defined edges. Unless
properly treated, range and height-of-burst errors may be introduced which are,
themselves, functions of range.
4) The speed of deformation during the early stages of the interaction is
a function of yield and height-of-burst. Analysis of this motion may provide an
independent burst height indicator although we anticipate that it will not be
particularly sensitive. Definition of scaling laws will require analysis of
two-dimensional calculations.
Figure 12 represents the analysis flow in a hypothetical system including
an iterative consideration of the effects of height-of-burst on ~lN. We are
currently implementing such an analysis scheme to test the validity of this
height-of-burst determination technique.
7
141 1 I I 1 8 1 I I 1 I 1 1 I I I I 1 I I I I.3
1.2
11
uPSHOT-KNOTHOLE /GRABLE Record 1798 I (Original)
1.1
1.0 0.9 : 0.8 ~
G
A 0.7 . ,, G
G * G *9 0.6 G
•b.~ 0.5 t t 0.4 , t 18/2
2m0a 0.3 tB/5
0.2
0.1 t 0.0 I 1 I 1 1 I 1 1 1 1 I 1 1 1 1 1 1 1 1 00 0.2 0.4 Ofi 0.8 1.0 1.2 1.4 1.6 1.8 2.o
TIME (StlC)
Fig. 3
Ratio of the vertical to the horizontal diameter as a function of time for GRABLE. GRABLE was a 15 kt explosion 160 m above the ground surface at the Nevada Test Site (NTS). t2~X is the calculated time of second thermal maximum while tB, the buoyancy time, is
given by R(t2AX) = g t?. R Examination of the GRABLE photographs s ows initial interaction at about 0.07 s although no substantial deformation occurs until about 0.1 s.
‘:v~q 1
1.0 “*:. . 0.9 :
0.8 :
A 0.7 t tR 0.6
0.5
0.4
0.3
0.2 I
. . .
G
G G .“. “ . G G
9 G
?
tfj/2
0.1
0.0 1 I I I I I 1 1 1 1 t I 1 1 1 1 1 I I 1 0.0 0.2 04 06 O.% I.0 1.2 1.4 16 1.8 20
TIME (see)
Fig. 4
FIZEAU was a 11.4 kt explosion at 152 meters. tR is the time of initial interaction determined from visual inspection of the photographic records.
8
1.4 I I 1 I 1 1 I I I I I I I I I I f I I
1.3 J 1.2
t
UPSHOT-KNOTHOLE/CLIMAX 1.1 Record 171081 (Originol)
1.0 &*. ~ 0.91 , “.. -1
0.8
I
t’= . A 0.7
G G .“ . .“
0.6 . .* .*
0.5 .**. .
G
04 1
0.3
0.2
[
f t~/5
o. I
t tB/2
0.01 I I I t I I I I I I I I I I I I I I 1
0.0 04 0s I
1.2 1.6 2.0 2.4 2B 3.2 3.6 40 TIME [see)
Fig. 5
CLIMAXwas a 63 kt explosion at 407 m burst height.
14 I I I I I t 1 I 1 I r I r I I I I I I
1.3 -1
A
I.2 -
1.1-
1.0-
0.9 -
0.8 -
0.7 -
0.6 -
0.5 -
04 -
0.3 t 0.2 t
TUMBLER-SNAPPER /OOG
Record 13382 (Print) . .
.
G
.
I
. . .
O.c.. J 1 1 1 I
2.4 2B J
3.2 3.6 4.0 TIME (WC)
Fig. 6
TS-DOG was 19 kt explosion at 317 m burst height.
9
1.31 1
1.2
1
EUSTER-JANGLE /EASY
I.1 Record 10942 (Print) 1
I.0 -“9.
G
0.9 - G8
G
0.8 - .
G ***-’ ‘
G
A 0.7 - G*
GG*.m .*
Q6 -
G .
G - G .** 0.3 - G
0.4 -
0.3 -
0.2 -
0.1 -
0.0 I 1 a I 1 1 1 I t 1 I I I 1 1 I 1 1 1
0.0 (14 OB 1.2 1.6 20 2.4 2.8 3.2 36 4.0
TIME (MC)
Fig. 7
BJ-EASY was a 31 kt explosion at 401 m. “~ ‘
1 I I I I I
1.3
1.2
1.1
1
1.0 G“” . .** 0.9 “ ‘
G
A o.8 G*
BUSTER- JANGLE/CHARLIE
Record 10742 (OrlgimIl)
1
0.7
I
G G ** G
0.6 t ‘**** ”*=””--” G G G
0.5 tR 0.4 ! tB/5 ? 0.3 t812 1 0.2 F 1
0.1
I 1 1 1 I 1 0.0 1 1 f 1 1 1 I I 1 1 1 I 1 1 0.0 0.4 OB I.2 1.6 20 2.4 2.8 3.2 3.6 40
TIME (see)
Fig. 8
BJ-CHARLIE was a 14 kt explosion at 345 meters burst height.
,
4
10
1.4“ I 1 I I I I 1 I I I i 1 I I 1 1 I I 1
1.3 -
1.2 - TEAPOT/ WASP-PRIME
1.I - Record 29339 (Print)
1.0 - .“”
0.9 - G***
G
0.8 - G . G 9 . 9 . . A 0.7 -
G . G **. G* . . .
G G=** 06 - 9.
0.5 -
0.4 -
0.3 -
0.2-
0.1-
0.0 1 t 1 1 1 1 1 1 1 I I 1 1 1 I I I 1 t
o 0.4 0.8 I .2 1.6 2.0 “2.4 2B 3.2 36 40
TIME (StiC)
Fig. 9
WASP PRIME was a 3 kt explosion at 222 m burst height.
DERIVEO HEIGHT
900. I I I I
800 -
700 -
600 -
500 -
400 -
1 300 -
200 -=
100 -
0 0 100200300400500600700 60090JJ
BURST HEIGHT
Fig. 10
For each of the seven Nevada test studied and one Pacific Test (DOMINIC AZTEC) the derived heights agree well with the actual heights. The range for each test indicated the height uncertainty produced by the uncertainty in the time of interaction.
11
,.
[
ed 12 A3900-woo A Bdll k1600-5600~ 9d 10 A5600- 6800 ~
Bd9 A8800-a240a
9d 8 A8240-Ioooo~
Bd 12
II
10
9
8
0 I00 200 m 400 500 Burst Height (m]
Fig. 11
Time of thermal minimum (tMIN) in Vi3riOUS
wavelength bands calculated for 540 kiloton explosions at various altitudes.
12
?
DIAMETER RATlO
4
I_
YIELD
- DIAMETER
d-
RANGE
A simplified
~
Fig. 12
block diagram of an analysis routine to determine burst height. The top three boxes contain data input into the analysis routine. Minimum time provides an initial yield estimate which may require modification due to burst height effects.